1. Field of the Invention
The present invention relates to systems and methods for distributed control of the inductive and capacitive loading of high voltage power transmission lines by using online injection modules that hang on or are connected to the power lines and are enabled for line balancing and distributed control.
2. Prior Art
Long transmission lines 102 of the power transmission system 100 shown in FIG. 1 are hung from transmission towers 101 and are used to transfer power, schematically shown as transferring power from generator 103 to load 104. These transmission lines, if long, can have a considerable shunt capacitance and series inductance, together with the transmission line resistance, which are distributed along the entire length of the line. Under these conditions, when the receiving-end power load is very small, or the circuit is open, the voltage at the receiving-end of the transmission line can rise to a level substantially higher than the voltage at the supply-end of the transmission line.
The foregoing effect is referred to as the Ferranti effect, and is caused by the combined effects of the distributed shunt capacitance and series inductance giving rise to a charging current in the transmission line. In particular, the transmission line 102 of FIG. 1 can be represented by the distributed π-model 200 shown in FIG. 2. FIG. 2 illustrates the power line with distributed resistance R 204 and inductance L 205 per unit length segment 201. Capacitance C 203 represents a shunt capacitance between the neighboring lines and ground.
Consider the lumped model of FIG. 3 which illustrates a lumped RLC circuit 300 representation of the distributed model 200 of the high voltage transmission line. FIG. 3 is a simplified representation of the high voltage transmission line drawing power from the supply side to the receiving side. Supply voltage {right arrow over (VR)} 206 has a shunt capacitance CS 302 and capacitive supply current {right arrow over (ICS)} 308 with ground. Receiving voltage {right arrow over (VR)} 207 has a shunt capacitance CR 303 and capacitive receiving current {right arrow over (ICR)} 309 with ground, in parallel with the LoadRL 312 having a load current {right arrow over (ILoad)} 311.
Now consider FIG. 4A, the phase diagram 400, and to most simply illustrate the Ferranti effect, consider the LoadRL 312 to be zero, that is the LoadRL 312 is open circuited (disconnected) with the load current {right arrow over (ILoad)} 311 equal to zero, then Vector {right arrow over (VR)} 207 represents the voltage at the receiving end of the transmission line, and appears across the capacitance CR 303. Because the AC current into a capacitor leads the AC voltage on the capacitor by 90 degrees, the AC current {right arrow over (ICR)} 309 in the transmission line leads the voltage on the capacitor CR, namely {right arrow over (VR)} 207, as shown in FIG. 4A. Thus the voltage drop in the line caused by the charging current for capacitor CR 303, being supplied through the line resistance R 304, is the voltage and {right arrow over (ΔVR)} 403 across resistor 304, is inphase with the charging current {right arrow over (ICR)} 309 as shown. That charging current also passes through the transmission line inductance L 305. Since the AC voltage in an inductor L leads the AC current on an inductor by 90 degrees, the voltage Δ{right arrow over (VL)} 404 across the inductor L is phase shifted another 90 degrees, as shown in the phase diagram 400. The net result is the voltage {right arrow over (VS)} 206, the voltage at the source end of the transmission line, which as can be seen in FIG. 4A, has a magnitude that is less than the voltage {right arrow over (VR)} 207 at the receiving end of the transmission line.
When the LoadRL 312 is not zero, the Ferranti effect does not disappear, but at least for substantial loads, the effects of the capacitive shunt current becomes masked by the dominance of the effects of the load current {right arrow over (ILoad)} 311, that is the resultant series inductive and resistive drops due the load current {right arrow over (ILoad)} 311 which is normally much larger than the drops due to the capacitive charging current at no-load conditions. The effects of the shunt capacitor charging current, under these conditions, tends to be lumped with the overall characteristics of the power distribution system for any corrections that may be attempted to maintain voltages, power factors, etc. within desirable limits.
It will be good to have an adaptive solution that can prevent or control the Ferranti effect from increasing the voltage at the receiving end of transmission lines when the load is reduced. What is proposed by the present invention is such a solution implemented using the distributed injection modules, which are also sometimes referred to as active impedance injection modules or distributed voltage/impedance injection modules that have been proposed by the parent applications of the current invention.